On Stein's Method of Moments and Generalized Score Matching

The Stein class used in method of moments parameter estimation has two functions whichneedtobespecified, forwhichthereisnopersuasiveargumentsforanyparticular choice. We show that by setting one to be the derivative of the density score function with respect to the parameter leads to a generalized score matching estimator with a choice of weight function. However, choosing a suitable weight function for generalized score matching is not straightforward. We show the weight function is equivalent to a transform of the data and using a score estimator, with an optimal transform being to a normal sample, using for example Box-Cox. We compare our proposal with an alternative means by which to handle the weight function, which is to use a generalized method of moment estimator.